Let's solve the
Area of a Circle worksheet step by step.
---
🔷 Formula for the Area of a Circle:
$$
\text{Area} = \pi \times r^2
$$
Where:
- $ r $ is the
radius of the circle
- $ \pi \approx 3.14 $ (we'll use this approximation unless otherwise specified)
> ⚠️
Note: The diagrams show a
diameter, not radius. So we need to
divide the diameter by 2 to get the radius.
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We’ll go through each problem:
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1. Diameter = 8 yd
- Radius $ r = \frac{8}{2} = 4 $ yd
- Area $ = \pi \times 4^2 = 3.14 \times 16 = 50.24 $ sq yd
✔ Answer: 50.24 yd²
---
2. Diameter = 18 in
- Radius $ r = \frac{18}{2} = 9 $ in
- Area $ = 3.14 \times 9^2 = 3.14 \times 81 = 254.34 $ sq in
✔ Answer: 254.34 in²
---
3. Diameter = 10 yd
- Radius $ r = \frac{10}{2} = 5 $ yd
- Area $ = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 $ sq yd
✔ Answer: 78.5 yd²
---
4. Diameter = 6 in
- Radius $ r = \frac{6}{2} = 3 $ in
- Area $ = 3.14 \times 3^2 = 3.14 \times 9 = 28.26 $ sq in
✔ Answer: 28.26 in²
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5. Diameter = 4 ft
- Radius $ r = \frac{4}{2} = 2 $ ft
- Area $ = 3.14 \times 2^2 = 3.14 \times 4 = 12.56 $ sq ft
✔ Answer: 12.56 ft²
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6. Diameter = 10 ft
- Radius $ r = \frac{10}{2} = 5 $ ft
- Area $ = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 $ sq ft
✔ Answer: 78.5 ft²
---
7. Diameter = 1 yd
- Radius $ r = \frac{1}{2} = 0.5 $ yd
- Area $ = 3.14 \times (0.5)^2 = 3.14 \times 0.25 = 0.785 $ sq yd
✔ Answer: 0.785 yd²
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8. Diameter = 14 in
- Radius $ r = \frac{14}{2} = 7 $ in
- Area $ = 3.14 \times 7^2 = 3.14 \times 49 = 153.86 $ sq in
✔ Answer: 153.86 in²
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9. Diameter = 2 yd
- Radius $ r = \frac{2}{2} = 1 $ yd
- Area $ = 3.14 \times 1^2 = 3.14 \times 1 = 3.14 $ sq yd
✔ Answer: 3.14 yd²
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✔ Final Answers:
| Problem | Area |
|--------|------|
| 1 | 50.24 yd² |
| 2 | 254.34 in² |
| 3 | 78.5 yd² |
| 4 | 28.26 in² |
| 5 | 12.56 ft² |
| 6 | 78.5 ft² |
| 7 | 0.785 yd² |
| 8 | 153.86 in² |
| 9 | 3.14 yd² |
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📝 Summary Tips:
- Always check if you're given
diameter or
radius.
- Divide diameter by 2 to get radius.
- Use $ \pi \approx 3.14 $ unless told otherwise.
- Remember units! Area is always in
square units (e.g., yd², in², ft²).
Let me know if you'd like this as a printable answer sheet! 😊
Parent Tip: Review the logic above to help your child master the concept of worksheet on circles.
